Abstract
Natural frequencies estimation of Francis turbines is of paramount importance in the stage of design in order to avoid vibration and resonance problems especially during transient events. Francis turbine runners are submerged in water and confined with small axial and radial gaps which considerably decrease their natural frequencies in comparison to the same structure in the air. Acoustic-structural FSI simulations have been used to evaluate the influence of these gaps. This model considers an entire prototype of a Francis turbine, including generator, shaft, runner and surrounding water. The radial gap between the runner and the static parts has been changed from the real configuration (about 0.04% the runner diameter) to 1% of the runner diameter to evaluate its influence on the machine natural frequencies. Mode-shapes and natural frequencies of the whole machine are discussed for all the boundary conditions tested.
Highlights
In order to satisfy the new market requirements for more dynamic and flexible energy generation, Francis turbines are demanded to increase their power concentration as well as their regulation capacity
The mesh of the generator and shaft is formed by 10-node tetrahedral elements (SOLID187 [10], see Fig. 3), whereas the mesh of the runner and surrounding water had to be constructed with 8-node hexahedral elements (SOLID185 for the runner and FLUID30 for the water) to consider the small gaps between the runner and static parts (g and h, see Fig. 4)
Water boundary conditions The nodes of the water that are in contact with the static parts are fixed without any displacement in all directions, whereas the nodes of the water in contact with the runner are defined as FSI (Fluid Structure Interaction) interface
Summary
In order to satisfy the new market requirements for more dynamic and flexible energy generation, Francis turbines are demanded to increase their power concentration as well as their regulation capacity. Francis turbine runners are rotating structures submerged in water and confined with small axial and radial gaps to the stationary parts The size of these gaps affects considerably the dynamic response of the runner, which is normally characterized by the runner’s natural frequencies and damping ratios associated to each mode-shape. Finite Element Method (FEM) models, together with acoustical formulation to consider the surrounding water, are capable to predict with precision the natural frequencies of submerged structures, even when they are near a rigid boundary [4, 5, 8] This kind of simulation does not consider complex terms such as damping; added damping due to the surrounding water is not taken into account. The specific speed of the Francis turbine is about ν=0.29 according to Eq (1) [4], being the nominal speed of the machine Ω=13.47 rad/s
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